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I have received the following file in this text format:

MULTILINESTRING((2513867.8515 5705794.4561,2512855.6784 5704240.0825,2511809.1121 5703060.1461,2507509.94
5707454.24,2513997.8033 5709971.3078,2513910.69 5709088.41,2513867.8515 5705794.4561)) 

How can I read this file and is there a way to convert coordinates from one projection to another using QGIS.

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    You have Well Known Text (WKT). Install WKT plugin for QGIS, create a new layer, paste WKT into layer, save as shapefile. – user30184 Feb 10 '17 at 12:20
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You can use Qgis for this. Layer -> add layer -> add delimited text layer

WKT to point

Then select Geometry definition as Well known text (WKT). Select first column as X and another as Y. That should creates you point layer i am not sure if it creates multiline too. If not just use Convert points to line(s) from SAGA toolbox.

SAGA

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